Despite recent advances in the analysis of graph data, it stays pretty challenging to define a meaningful distance between graphs. Instead of comparing graphs directly, we therefore propose to look at the signal distributions governed by graph filters. Specifically, we define the filter graph distance (fGOT) as a generalisation of the graph optimal transport (GOT) distance proposed by [1]}, which has the ability to emphasise specific spectral properties of the graph, such as high or low frequencies, local or global graph phenomena. We model these properties through filtered graph signals, which exploit the specific graph information and evenutally compare graphs through filtered signal distributions.
